# Contextual Dynamic Pricing with Strategic Buyers

arXiv: https://arxiv.org/abs/2307.04055 · HTML: https://mlsanity.com/paper/2307.04055/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 66 references that are in the map.
- First posted on arXiv 8 Jul 2023.

## Builds on (most cited first, 27 of 27)

- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [High-Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2011.04020/) (2020)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Meta Dynamic Pricing: Transfer Learning Across Experiments](https://mlsanity.com/paper/1902.10918/) (2019)
- [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020)
- [Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process](https://mlsanity.com/paper/2202.10589/) (2022)
- [Strategic Classification under Unknown Personalized Manipulation](https://mlsanity.com/paper/2305.16501/) (2023)
- [Policy Optimization Using Semi-parametric Models for Dynamic Pricing](https://mlsanity.com/paper/2109.06368/) (2021)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (2021)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise](https://mlsanity.com/paper/2201.11341/) (2022)
- [Perishability of Data: Dynamic Pricing under Varying-Coefficient Models](https://mlsanity.com/paper/1701.03537/) (2017)
- [Minimax-Optimal Multi-Agent RL in Markov Games With a Generative Model](https://mlsanity.com/paper/2208.10458/) (2022)
- [Bayesian Persuasion for Algorithmic Recourse](https://mlsanity.com/paper/2112.06283/) (2021)
- [Incentive-aware Contextual Pricing with Non-parametric Market Noise](https://mlsanity.com/paper/1911.03508/) (2019)
- [Performative Prediction with Bandit Feedback: Learning through Reparameterization](https://mlsanity.com/paper/2305.01094/) (2023)
- [Fairness-aware Online Price Discrimination with Nonparametric Demand Models](https://mlsanity.com/paper/2111.08221/) (2021)
- [Crowd-assisted Search for Price Discrimination in E-Commerce: First results](https://mlsanity.com/paper/1307.4531/) (2013)
- [Online Regularization towards Always-Valid High-Dimensional Dynamic Pricing](https://mlsanity.com/paper/2007.02470/) (2020)
- [High-Dimensional Dynamic Pricing under Non-Stationarity: Learning and Earning with Change-Point Detection](https://mlsanity.com/paper/2303.07570/) (2023)

## Built on by (most cited first, 3 of 3)

- [Practical Performative Policy Learning with Strategic Agents](https://mlsanity.com/paper/2412.01344/) (2024)
- [Microfoundation Inference for Strategic Prediction](https://mlsanity.com/paper/2411.08998/) (2024)
- [COBRA: Contextual Bandit Algorithm for Ensuring Truthful Strategic Agents](https://mlsanity.com/paper/2505.23720/) (2025)

## Abstract (arXiv)

Personalized pricing, which involves tailoring prices based on individual characteristics, is commonly used by firms to implement a consumer-specific pricing policy. In this process, buyers can also strategically manipulate their feature data to obtain a lower price, incurring certain manipulation costs. Such strategic behavior can hinder firms from maximizing their profits. In this paper, we study the contextual dynamic pricing problem with strategic buyers. The seller does not observe the buyer's true feature, but a manipulated feature according to buyers' strategic behavior. In addition, the seller does not observe the buyers' valuation of the product, but only a binary response indicating whether a sale happens or not. Recognizing these challenges, we propose a strategic dynamic pricing policy that incorporates the buyers' strategic behavior into the online learning to maximize the seller's cumulative revenue. We first prove that existing non-strategic pricing policies that neglect the buyers' strategic behavior result in a linear Omega(T) regret with T the total time horizon, indicating that these policies are not better than a random pricing policy. We then establish that our proposed policy achieves a sublinear regret upper bound of O(√T). Importantly, our policy is not a mere amalgamation of existing dynamic pricing policies and strategic behavior handling algorithms. Our policy can also accommodate the scenario when the marginal cost of manipulation is unknown in advance. To account for it, we simultaneously estimate the valuation parameter and the cost parameter in the online pricing policy, which is shown to also achieve an O(√T) regret bound. Extensive experiments support our theoretical developments and demonstrate the superior performance of our policy compared to other pricing policies that are unaware of the strategic behaviors.